# Question 1: (Bonds, 10 points)

(a). (4 points) Find the price of a 10% Government coupon bond that pays annual coupons, matures in exactly 2 years, and has a face value of \$1,000. The yield to maturity is 9% p.a. compounded annually. The first coupon that you will receive is due in exactly one year.
(b). (6 points) In addition to the coupon bond in part (a) you observe two more Government coupon bonds that will also mature in 2 years from now, both with a face value of 1,000 dollars. These two coupon bonds are identical to the bond in part (a) except for the fact that their coupon rates are 8% and 12%, respectively. The prices of these bonds are given below:

 Time to Maturity  (years) Coupon rate Face value Price 2 8% 1,000 965.29 2 12% 1,000 1034.71

Are the prices of these two coupon bonds consistent with the price of the coupon bond from part (a)? Explain your answer. If the prices are inconsistent show, in detail, how you can make riskless arbitrage profits. The three bonds may be bought or sold in any amounts. Organize all transactions, profits, and the resulting payoffs in an arbitrage table.

# Question 2: (Stocks, 20 points)

BLUE, Inc., an all-equity firm, will have earnings per share next year of \$4. The company pays 40% of its earnings as dividends. The required rate of return for the firm is 16%, and the expected growth rate of future earnings is 12%. The risk-free interest rate is 10%.
(c). (6 Points) Compute the current stock price of BLUE, Inc. and the prospective dividend yield.
(d). (7 Points) The management at BLUE Inc. has decided to adopt a drastic change to the company’s operations, which will in turn alter their dividend payments. Specifically, they now expect to pay dividends of \$3, \$5, and \$7 dollars for the next three years, after which the dividend is expected to grow at 8% in perpetuity. As in part (c), assume that the first dividend will be paid exactly one year from today and that the required rate of return on equity is 16%. Compute the company’s new stock price based on the revised plan.
(e). (7 points) The company has decided to change from annual to bi-annual (i.e. every other year) dividend payments after the dividend in year 3 is paid (so that the next dividend will occur in year 5). Compute the annualized dividend growth rate necessary to maintain the current stock price (P0) that you found in part (d).

# Question 3: (Portfolio Analysis, 16 points)

You consider investing in two stocks, NEWcom and OLDcom, with the following characteristics: The stocks are valued in a market where investors can borrow and lend, using T-bills, at the risk-free rate of 5%. The market portfolio risk premium is 8%.

 NEWcom OLDcom Beta (b) 0.8 1.2 Standard Deviation of returns (s) 0.20 0.32

(f). (6 points) Compute the expected returns and Sharpe ratios for both NEWcom and OLDcom.
(g). (6 points) If you can only invest in either T-bills and NEWcom, or T-bills and OLDcom, what is the lowest risk portfolio that gives you an expected return of 14.6%? What is the standard deviation of this portfolio?
(h). (4 Points) Suppose that you can lend at the risk-free rate of 5% but are forced to borrow at 7% because of credit concerns. What is the lowest risk portfolio with an expected return of 14.6%? As in part (b) you can combine borrowing or lending with either NEWcom or OLDcom.

# Question 4: (CAPM, 18 points)

The expected return and standard deviation of the S&P500, which you may assume is the market portfolio, are 16% and 25% per year, respectively. The expected return to IBM is unknown, but it has a correlation of 0.8 with the S&P500 and a standard deviation equal to 50%. Assume that the risk-free rate is given by the return on short-term T-bills, which currently yield 6%.
(i). (4 points) Compute IBM’s beta and expected return.
(j). (3 points) If AMD’s expected return is half that of IBM’s, what is AMD’s beta?
(k). (5 points) Calculate the beta and expected return of the following portfolio.

 Asset Portfolio Weight IBM 0.45 AMD -0.30 S&P500 0.75 T-Bill 0.10

(l). (6 points) Does the portfolio in part (k) lie on the capital market line? If so, explain why this is the case. If not, find another portfolio offering the same expected return but with less risk, being sure to specify the assets in your portfolio and their weights.

# Question 5: (Capital Budgeting, 14 points)

(m). A bicycle manufacturer currently produces 300,000 units a year and expects output levels to remain steady in the future. It buys chains from an outside supplier at a price of \$2 a chain. The plant manager believes that it would be cheaper to make these chains rather than buy them. Direct in-house production costs are estimated to be only \$1.50 per chain. The necessary machinery would cost \$250,000 and would be obsolete after 10 years. This investment could be depreciated to zero for tax purposes using a 10-year straight-line depreciation schedule. The plant manager estimates that the operation would require additional working capital of \$50,000 but argues that this sum can be ignored since it is recoverable at the end of the 10 years. Expected proceeds from scrapping the machinery after 10 years are \$20,000.
If the company pays tax at a rate of 35% and the opportunity cost of capital is 15%, what is the net present value of the decision to produce the chains in-house instead of purchasing them from the supplier?

# Question 6: (Leverage, 22 points)

The Learning Rainbow has the following capital structure:

 Security Beta Total Market Value(millions of dollars) Debt 0 100 Preferred Stock 0.2 40 Common Stock 1.2 200

(n). (4 points) What is the Learning Rainbow’s asset beta?
(o). (4 points) How would the asset beta change if the Learning Rainbow issued an additional \$140 million of common stock and used the cash to repurchase all the debt and preferred stock?
(p). (4 points) What discount rate should the Learning Rainbow set for investments that expand the scale of its operations without changing its asset beta? Assume that the CAPM holds and that new investment is equity-financed. The risk free rate is 5% and the expected return on the market is 13%.
(q). (6 points) How would the asset beta change if the Learning Rainbow issued an additional \$140 million of common stock and used 100 million of the cash to repurchase the debt and 40 million to purchase additional assets with a beta equal to 1.4?
(r). (4 points) Given the information provided in part (d), what is the new common stock beta if the preferred stock market value and beta remain unchanged?

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